共查询到20条相似文献,搜索用时 78 毫秒
1.
C.L. Prather 《Journal of Mathematical Analysis and Applications》2009,349(1):55-67
Let L=(1−x2)D2−((β−α)−(α+β+2)x)D with , and . Let f∈C∞[−1,1], , with normalized Jacobi polynomials and the Cn decrease sufficiently fast. Set Lk=L(Lk−1), k?2. Let ρ>1. If the number of sign changes of (Lkf)(x) in (−1,1) is O(k1/(ρ+1)), then f extends to be an entire function of logarithmic order . For Legendre expansions, the result holds with replaced with . 相似文献
2.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2009,349(2):436-442
Consider the eigenvalue problem : −Δu=λf(x,u) in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN. Denote by the set of all Carathéodory functions f:Ω×R→R such that for a.e. x∈Ω, f(x,⋅) is Lipschitzian with Lipschitz constant L, f(x,0)=0 and , and denote by (resp. ) the set of λ>0 such that has at least one nonzero classical (resp. weak) solution. Let λ1 be the first eigenvalue for the Laplacian-Dirichlet problem. We prove that and . Our result is a positive answer to Ricceri's conjecture if use f(x,u) instead of f(u) in the conjecture. 相似文献
3.
Saroj Kumar Dash 《Journal of Mathematical Analysis and Applications》2008,339(1):98-107
For a symmetric stable process X(t,ω) with index α∈(1,2], f∈Lp[0,2π], p?α, and , we establish that the random Fourier-Stieltjes (RFS) series converges in the mean to the stochastic integral , where fβ is the fractional integral of order β of the function f for . Further it is proved that the RFS series is Abel summable to . Also we define fractional derivative of the sum of order β for an, An(ω) as above and . We have shown that the formal fractional derivative of the series of order β exists in the sense of mean. 相似文献
4.
5.
Let R be a commutative local noetherian ring, and let L and L′ be R-modules. We investigate the properties of the functors and . For instance, we show the following:
- (a)
- if L and L′ are artinian, then is artinian, and is noetherian over the completion ;
- (b)
- if L is artinian and L′ is Matlis reflexive, then , , and are Matlis reflexive.
6.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
7.
Dikran Dikranjan Dmitri Shakhmatov 《Journal of Mathematical Analysis and Applications》2010,363(1):42-330
For an abelian topological group G, let denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X)<w(G), and an open neighborhood U of 0 in T, we show that . (Here, w(G) denotes the weight of G.) A subgroup D of G determines G if the map defined by r(χ)=χ?D for , is an isomorphism between and . We prove that
8.
Roman Sznajder 《Journal of Mathematical Analysis and Applications》2003,279(2):617-624
Given a function f on Rn, we introduce the concept of anisotropic regularization as a generalization of Tikhonov regularization fε(x)=f(x)+εx. When f is a continuous -function on Rn and K is a box in Rn, we study the properties of and the limiting behavior of solutions of a regularized box variational inequality problem , with emphasis on the existence of weak Pareto minimal points with respect to K. This work generalizes results of Sznajder and Gowda (1998) proved in the setting of nonlinear complementarity problems. 相似文献
9.
Yuan Li 《Journal of Mathematical Analysis and Applications》2011,382(1):172-3242
Let ?A be a normal completely positive map on B(H) with Kraus operators . Denote M the subset of normal completely positive maps by . In this note, the relations between the fixed points of ?A and are investigated. We obtain that , where K(H) is the set of all compact operators on H and is the dual of ?A∈M. In addition, we show that the map is a bijection on M. 相似文献
10.
Marcus Wagner 《Journal of Mathematical Analysis and Applications》2009,355(2):606-619
Assume that K⊂Rnm is a convex body with o∈int(K) and is a function with f|K∈C0(K,R) and f|(Rnm?K)≡+∞. We show that its lower semicontinuous quasiconvex envelope
11.
Let p∈(1,∞), q∈[1,∞), s∈R and . In this paper, the authors establish the φ-transform characterizations of Besov-Hausdorff spaces and Triebel-Lizorkin-Hausdorff spaces (q>1); as applications, the authors then establish their embedding properties (which on is also sharp), smooth atomic and molecular decomposition characterizations for suitable τ. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in and (q>1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p∈(1,∞) and q∈[1,∞) by taking τ=0. 相似文献
12.
Constantin Tudor 《Journal of Mathematical Analysis and Applications》2009,351(1):456-468
The domain of the Wiener integral with respect to a sub-fractional Brownian motion , , k≠0, is characterized. The set is a Hilbert space which contains the class of elementary functions as a dense subset. If , any element of is a function and if , the domain is a space of distributions. 相似文献
13.
Ke-Ang Fu 《Journal of Mathematical Analysis and Applications》2009,356(1):280-287
Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively. 相似文献
14.
Yuan Zhou 《Journal of Mathematical Analysis and Applications》2011,382(2):577-593
The author establishes some geometric criteria for a Haj?asz-Sobolev -extension (resp. -imbedding) domain of Rn with n?2, s∈(0,1] and p∈[n/s,∞] (resp. p∈(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α∈(0,1) if and only if for some/all s∈[α,1) and p=(2−α)/(s−α), where denotes the restriction of the Triebel-Lizorkin space on Ω. 相似文献
15.
In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces . The authors also establish an equivalent characterization of when τ∈[0,1/p). These Besov-type spaces and Triebel-Lizorkin-type spaces were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces and , the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ=0. 相似文献
16.
Katerina Saneva 《Journal of Mathematical Analysis and Applications》2010,370(2):543-554
We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S0(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients. 相似文献
17.
Bernard K. Bonzi 《Journal of Mathematical Analysis and Applications》2010,370(2):392-405
We study the boundary value problem in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN (N?3) and is a p(x)-Laplace type operator with p(.):Ω→[1,+∞) a measurable function and b a continuous and nondecreasing function from R→R. We prove the existence and uniqueness of an entropy solution for L1-data f. 相似文献
18.
Rafa? Filipów 《Journal of Mathematical Analysis and Applications》2010,362(1):64-71
We consider ideals I of subsets of the set of natural numbers such that for every conditionally convergent series ∑n∈ωan and every there is a permutation such that ∑n∈ωaπr(n)=r and
19.
Vyacheslav V. Chistyakov Yuliya V. Tretyachenko 《Journal of Mathematical Analysis and Applications》2010,369(1):82-93
Given a=(a1,…,an), b=(b1,…,bn)∈Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), denote by the Hildebrandt-Leonov total variation of f on , which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted for publication]. The following Helly-type pointwise selection principle is proved: If a sequence{fj}j∈Nof maps frominto M is such that the closure in M of the set{fj(x)}j∈Nis compact for eachandis finite, then there exists a subsequence of{fj}j∈N, which converges pointwise onto a map f such that. A variant of this result is established concerning the weak pointwise convergence when values of maps lie in a reflexive Banach space (M,‖⋅‖) with separable dual M∗. 相似文献
20.
This paper is concerned with the well-posedness of the Navier-Stokes-Nerst-Planck-Poisson system (NSNPP). Let sp=−2+n/p. We prove that the NSNPP has a unique local solution for in a subspace, i.e., Vu1×Vv1×Vv1, of with . We also prove that there exists a unique small global solution for any small initial data with . 相似文献